/*
 * Class:        OrnsteinUhlenbeckProcess
 * Description:  
 * Environment:  Java
 * Software:     SSJ 
 * Copyright (C) 2001  Pierre L'Ecuyer and Universite de Montreal
 * Organization: DIRO, Universite de Montreal
 * @author       
 * @since

 * SSJ is free software: you can redistribute it and/or modify it under
 * the terms of the GNU General Public License (GPL) as published by the
 * Free Software Foundation, either version 3 of the License, or
 * any later version.

 * SSJ is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.

 * A copy of the GNU General Public License is available at
   <a href="http://www.gnu.org/licenses">GPL licence site</a>.
 */
package umontreal.ssj.stochprocess;
import umontreal.ssj.rng.*;
import umontreal.ssj.probdist.*;
import umontreal.ssj.randvar.*;

/**
 * This class represents an *Ornstein-Uhlenbeck* process @f$\{X(t) : t \geq0
 * \}@f$, sampled at times @f$0 = t_0 < t_1 < \cdots< t_d@f$. This process
 * obeys the stochastic differential equation
 * @anchor REF_stochprocess_OrnsteinUhlenbeckProcess_eq_ornstein
 * @f[
 *   dX(t) = \alpha(b - X(t)) dt + \sigma  dB(t) \tag{ornstein}
 * @f]
 * with initial condition @f$X(0)= x_0@f$, where @f$\alpha@f$, @f$b@f$ and
 * @f$\sigma@f$ are positive constants, and @f$\{B(t),  t\ge0\}@f$ is a
 * standard Brownian motion (with drift 0 and volatility 1). This process is
 * *mean-reverting* in the sense that it always tends to drift toward its
 * general mean @f$b@f$. The process is generated using the sequential
 * technique @cite fGLA04a&thinsp; (p. 110)
 * @anchor REF_stochprocess_OrnsteinUhlenbeckProcess_eq_ornstein_seq
 * @f[
 *   X(t_j) = e^{-\alpha(t_j - t_{j-1})} X(t_{j-1}) + b\left(1 - e^{-\alpha(t_j - t_{j-1})}\right) + \sigma\sqrt{\frac{1 - e^{-2\alpha(t_j - t_{j-1})}}{2\alpha}}  Z_j \tag{ornstein-seq}
 * @f]
 * where @f$Z_j \sim N(0,1)@f$. The time intervals @f$t_j - t_{j-1}@f$ can be
 * arbitrarily large.
 *
 * <div class="SSJ-bigskip"></div><div class="SSJ-bigskip"></div>
 */
public class OrnsteinUhlenbeckProcess extends StochasticProcess {
    protected NormalGen    gen;
    protected double       alpha,
                           beta,
                           sigma;
    // Precomputed values 
    protected double[]     badt,
                           alphadt,
                           sigmasqrdt;

   /**
    * Constructs a new `OrnsteinUhlenbeckProcess` with parameters
    * @f$\alpha=@f$ `alpha`, @f$b@f$, @f$\sigma=@f$ `sigma` and initial
    * value @f$X(t_0) =@f$ `x0`. The normal variates @f$Z_j@f$ will be
    * generated by inversion using the stream `stream`.
    */
   public OrnsteinUhlenbeckProcess (double x0, double alpha, double b,
                                    double sigma, RandomStream stream) {
        this (x0, alpha, b, sigma, new NormalGen (stream));
    }

   /**
    * Here, the normal variate generator is specified directly instead of
    * specifying the stream. The normal generator `gen` can use another
    * method than inversion.
    */
   public OrnsteinUhlenbeckProcess (double x0, double alpha, double b,
                                    double sigma, NormalGen gen) {
      this.alpha = alpha;
      this.beta  = b;
      this.sigma = sigma;
      this.x0    = x0;
      this.gen   = gen;
   }


   public double nextObservation() {
        double xOld = path[observationIndex];
        double x = badt[observationIndex] + xOld * alphadt[observationIndex]
                   + sigmasqrdt[observationIndex] * gen.nextDouble();
        observationIndex++;
        path[observationIndex] = x;
        return x;
    }

/**
 * Generates and returns the next observation at time @f$t_{j+1} =@f$
 * `nextTime`, using the previous observation time @f$t_j@f$ defined earlier
 * (either by this method or by <tt>setObservationTimes</tt>), as well as the
 * value of the previous observation @f$X(t_j)@f$. *Warning*: This method
 * will reset the observations time @f$t_{j+1}@f$ for this process to
 * `nextTime`. The user must make sure that the @f$t_{j+1}@f$ supplied is
 * @f$\geq t_j@f$.
 */
public double nextObservation (double nextTime) {
        double previousTime = t[observationIndex];
        double xOld = path[observationIndex];
        observationIndex++;
        t[observationIndex] = nextTime;
        double dt = nextTime - previousTime;
        double tem = Math.exp(-alpha * dt);
        double tem1 = -Math.expm1(-alpha * dt);
        double x = tem*xOld + beta*tem1 + sigma *
            Math.sqrt(tem1*(1.0 + tem)/(2.0*alpha)) * gen.nextDouble();
        path[observationIndex] = x;
        return x;
    }

   /**
    * Generates an observation of the process in `dt` time units, assuming
    * that the process has value @f$x@f$ at the current time. Uses the
    * process parameters specified in the constructor. Note that this
    * method does not affect the sample path of the process stored
    * internally (if any).
    */
   public double nextObservation (double x, double dt) {
        double tem = Math.exp(-alpha * dt);
        double tem1 = -Math.expm1(-alpha * dt);
        x = tem*x + beta*tem1 + sigma *
            Math.sqrt(tem1*(1.0 + tem)/(2.0*alpha)) * gen.nextDouble();
        return x;
    }
public double[] generatePath() {
        double x;
        double xOld = x0;
        for (int j = 0; j < d; j++) {
            x = badt[j] + xOld * alphadt[j] + sigmasqrdt[j] * gen.nextDouble();
            path[j + 1] = x;
            xOld = x;
        }
        observationIndex = d;
        return path;
    }

/**
 * Generates a sample path of the process at all observation times, which are
 * provided in array `t`. Note that `t[0]` should be the observation time of
 * `x0`, the initial value of the process, and `t[]` should have at least
 * @f$d+1@f$ elements (see the `setObservationTimes` method).
 */
public double[] generatePath (RandomStream stream) {
        gen.setStream (stream);
        return generatePath();
    }

   /**
    * Resets the parameters @f$X(t_0) =@f$ `x0`, @f$\alpha=@f$ `alpha`,
    * @f$b =@f$ `b` and @f$\sigma=@f$ `sigma` of the process. *Warning*:
    * This method will recompute some quantities stored internally, which
    * may be slow if called too frequently.
    */
   public void setParams (double x0, double alpha, double b, double sigma) { 
        this.alpha = alpha;
        this.beta  = b;
        this.sigma = sigma;
        this.x0    = x0;
        if (observationTimesSet) init(); // Otherwise not needed.
    }

   /**
    * Resets the random stream of the normal generator to `stream`.
    */
   public void setStream (RandomStream stream) { gen.setStream (stream); }

   /**
    * Returns the random stream of the normal generator.
    */
   public RandomStream getStream () { return gen.getStream (); }

   /**
    * Returns the value of @f$\alpha@f$.
    */
   public double getAlpha() { return alpha; }

   /**
    * Returns the value of @f$b@f$.
    */
   public double getB() { return beta; }

   /**
    * Returns the value of @f$\sigma@f$.
    */
   public double getSigma() { return sigma; }

   /**
    * Returns the normal random variate generator used. The `RandomStream`
    * used for that generator can be changed via
    * `getGen().setStream(stream)`, for example.
    */
   public NormalGen getGen() { return gen; }


   protected void initArrays(int d) {
      double dt, tem, tem1;
      for (int j = 0; j < d; j++) {
         dt = t[j+1] - t[j];
         tem = Math.exp(-alpha * dt);
         tem1 = -Math.expm1(-alpha * dt);
         badt[j] = beta*tem1;
         alphadt[j] = tem;
         sigmasqrdt[j] = sigma * Math.sqrt (tem1*(1.0 + tem)/(2.0*alpha));
      }
   }

    // This is called by setObservationTimes to precompute constants
    // in order to speed up the path generation.
    protected void init() {
        super.init();
        badt = new double[d];
        alphadt = new double[d];
        sigmasqrdt = new double[d];
        initArrays(d);
     }

}